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Expression of type Equals

from the theory of proveit.physics.quantum.algebra

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import A, alpha, beta, gamma
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals
from proveit.numbers import Mult
from proveit.physics.quantum import Qmult, ket_psi
In [2]:
# build up the expression from sub-expressions
expr = Equals(Qmult(alpha, ScalarMult(beta, Qmult(A)), ket_psi, gamma), ScalarMult(Mult(alpha, beta, gamma), Qmult(A, ket_psi)))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\alpha \thinspace \left(\beta \cdot \left[A\right]\right) \thinspace \lvert \psi \rangle \thinspace \gamma\right) = \left(\left(\alpha \cdot \beta \cdot \gamma\right) \cdot \left(A \thinspace \lvert \psi \rangle\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 20
operands: 5
4Operationoperator: 10
operands: 6
5ExprTuple16, 7, 19, 18
6ExprTuple8, 9
7Operationoperator: 10
operands: 11
8Operationoperator: 12
operands: 13
9Operationoperator: 20
operands: 14
10Literal
11ExprTuple17, 15
12Literal
13ExprTuple16, 17, 18
14ExprTuple24, 19
15Operationoperator: 20
operand: 24
16Variable
17Variable
18Variable
19Operationoperator: 22
operand: 25
20Literal
21ExprTuple24
22Literal
23ExprTuple25
24Variable
25Variable